Kite Area Calculator

Created by Gabriela Diaz
Last updated: Jul 09, 2022

Use the kite area calculator to determine the area and perimeter of a kite. This tool presents two ways for calculating the area of the kite: with the diagonals or with the two non-equal sides and the angle between them.

If you'd like to learn more about how to find the area of a kite and its perimeter, you might want to keep reading the following text, where you'll also find:

  • The kite area formulas
  • Is a kite a rhombus?; and
  • The kite perimeter formula.

Enjoy 🪁

How to find the area of a kite — Kite area formula

Depending on the information available, there are two approaches to determining the area of a kite. Let's take a look at them:

With the diagonals

If the kite's diagonals are known, you can use the general formula for the area of an orthogonal quadrilateral to calculate the area of a kite. An orthogonal quadrilateral is a type of quadrilateral with diagonals that cross at right angles. The formula in this case is:

A=e×f2\small A = \cfrac{e \times f}{2}

where:

  • AA — Area of a kite; and
  • ee and ff — Diagonals of the kite.
Kite with diagonals e and f

This is the same formula used to calculate a rhombus's area. A rhombus, like a kite, is a particular case of an orthogonal quadrilateral, having two pairs of parallel sides and four equal-length sides. A rhombus is equivalent to a square when the angles between sides are right angles.

So, is a kite a rhombus? As you might be able to tell from the abovementioned, the answer is that all rhombuses are kites, but not all kites are rhombuses.

With two non-equal sides and the angle between them

The other way to determine the area of a kite is with the lengths of two non-congruent side lengths and the size of the angle between those two sides. The formula in this case is:

A=a×b×sin(α)\small A = a \times b \times sin(\alpha)

where:

  • AA — Area of the kite;
  • aa and bb — Non-equal sides; and
  • α\alpha — Angle between non-equal sides.

The inverse function of the sine is the arcsine. If you'd like to learn more about this function, you might want to visit our acsine calculator 📐

Kite with sides a and b and angle α between them

If the formula above looks familiar, it's because it's derived from the area formula of a SAS triangle, also known as a side-angle-side triangle. A kite may alternatively be seen as two congruent triangles that are mirror images of one another. Multiplying the formula for the area of a single triangle by two provides the equation above.

Find the perimeter of a kite

To calculate the perimeter of a kite, you need to know the value of its two non-equal sides. To find the perimeter using the following formula:

P=2×(a+b)\small P = 2 \times (a + b)

where:

  • PP — Perimeter of the kite; and
  • aa and bb — Non-equal sides of the kite.

It's not possible to calculate the perimeter with the diagonals. Even though we know that one diagonal is a perpendicular bisector of the other, we don't know where the intersection is.

How to use the kite area calculator

With the kite area calculator, you can determine both the area and perimeter of a kite.

This tool provides you with two alternatives for calculating the area. You can determine it with the diagonals or with two unequal sides and the angle between them. Let's look at how to do these calculations using the kite area calculator:

From two diagonals:

  1. If you know the length of the kite's diagonals, choose from the Given field the two diagonals option.

  2. Proceed to enter the values of the diagonals e and f in their corresponding fields.

  3. The calculator will now display the kite's Area.

  4. To obtain the Perimeter of the kite, enter the lengths of the sides a and b.

From two unequal sides and the angle between:

  1. To obtain the area and perimeter of a kite, knowing the values of two unequal sides and the angle between them, select from the Given field the two unequal sides and the angle option.

  2. By entering the values of the sides a and b, the calculator will be able to determine the Perimeter of the kite.

  3. In order to obtain the kite's Area, enter the value of the Angle α in the respective field.

If you enjoyed using this tool and would like to learn more about quadrangle shapes, you might be interested in checking the trapezoid calculator 📐

Gabriela Diaz
Given
two diagonals
kite with diagonals e and f





e
in
f
in
Area
in²
Perimeter
a
in
b
in
Perimeter
in
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